Solve the problem.
-The resistance of a wire varies directly as its length and inversely as the square of its diameter. A 50 -ft wire with a $0.4$-in. diameter has a resistance of $0.0125 \Omega$. Find the resistance of a 20 -ft wire with a diameter of $0.1$-in. Round to 4 decimal places if necessary.
A) $0.0800 \Omega$
B) $0.0100 \Omega$
C) $0.3162 \Omega$
D) $0.0025 \Omega$

Question

Quizplus · Accepted Answer

The resistance of a wire varies directly as its length and inversely as the square of its diameter. So, the resistance of a wire can be expressed as R = k(L/d^2), where k is a constant. We can find the value of k by using the given information: R = 0.0125 ohms, L = 50 ft, and d = 0.4 in. Substituting these values into the equation, we get: 0.0125 = k(50/0.4^2). Solving for k, we get: k = 0.000025. Now we can use this value of k to find the resistance of a 20-ft wire with a diameter of 0.1 in: R = k(L/d^2) = 0.000025(20/0.1^2) = 0.08 ohms.

Solve the Problem 0.40.40.4 -In Diameter Has a Resistance Of a Wire

Solve the Problem $0.4$ -In Diameter Has a Resistance Of a Wire